Many thanks to Seamus for providing an excellent analysis of the debt rule. At the risk of overkill, I think it is useful to offer one further angle.
One aspect of the debt (i.e. 1/20th) rule that may not be fully appreciated it that it is – like the 3 percent deficit rule – a trigger for the Excessive Deficit Procedure (EDP). In the past, the trigger for the EDP was a deficit greater than 3 percent of GDP. With the revised Stability and Growth Pact, the EDP can be triggered either by an excessive deficit or an insufficient rate of reduction in the debt to GDP ratio. This fact is important for reasons that link to the discussion about the uncertainty surrounding growth prospects across recent threads.
To see this, it is useful to recast both the deficit and debt-reduction rules in a way that makes them more easily comparable. (I will make some approximations to make the maths a bit more digestible, but they don’t change the basic message.)
The equation for the change in the debt to GDP ratio can be approximated by,
Δd = (i – g)d-1 – ps,
where d is the debt to GDP ratio (in percent of GDP), i is the average nominal interest rate on outstanding debt, g is the nominal growth rate, d-1 is last year’s debt to GDP ratio (in percent of GDP), ps is the primary surplus (in percent of GDP), and Δ represents the change in a variable (measured in percentage points of GDP).
Noting that the overall deficit as a percent of GDP (denoted def) can be written as id-1 – ps, we can rewrite the equation as
Δd = def – gd-1.
The 3 percent deficit rule says that the deficit must be below 3 percent of GDP. Using the last equation, we can rewrite the deficit rule as a debt reduction rule,
Δd < 3 – gd-1.
Ignoring the averaging procedure that Seamus details in his post below to keep things simple, we can write the debt reduction rule as,
Δd < (1/20)(60 – d-1) = 3 – 0.05d-1.
Both rules take a surprisingly similar form. Given the existence of deficit rule, the debt-reduction rule only binds on fiscal policy (in the sense of triggering an EDP) if the nominal growth rate is less the 5 percent per year. (Note this is consistent with Seamus’s calculations given that the deficit is projected to fall below 3 pecent of GDP in 2015.)
(As an aside, some commentators have noted the superiority of debt-reduction rules over deficit rules. I agree with this as a general principle. But it is not necessarily the case when it comes to comparing the particular rules we have above. The deficit rule has the advantage of being “growth contingent”: the implied required rate of debt reduction falls as the growth rate falls. The debt-reduction rule is insensitive to the rate of economic growth. I see the growth contingency as an attractive feature of the deficit rule.)
While noting yet again that the debt rule is already in place under the revised SGP and so not new to the fiscal compact, critics of the rule have a point when they draw attention to possible drastic implications of the rule in a very low-growth scenario. (In our previous posts, both Seamus and I took existing projections from the IMF and Government (SPU). These projections are based on a return to reasonable growth rates. But there is downside risk to these relatively benign growth scenarios.)
This is where the fact that the debt-reduction rule is a trigger for the EDP becomes so important. If the rule actually forced debt reductions according to the third equation above, the results could be catastrophic. To take an extreme case, if nominal growth was zero percent and the debt to GDP ratio was 120 percent, then the rule would require that the debt to GDP ratio is lowered at the rate of 3 percentage points per year.
This would be crazy in the context of zero growth; it would require a overall surplus of 3 percent of GDP and a primary surplus of about 9 percent of GDP. But it is not what would happen. If the rule is not met the country would enter the EDP. Under the EDP, a deficit reduction path would be worked out that would balance the need to move towards compliance with the need to phase the adjustment over time. The fact that what the debt-reduction rule does is trigger the EDP is a critical fact in understanding the implications of the rules.
Note: The post has been corrected for an error in the original version.